The 23-year-old victim was found with severe facial injuries in a play area at Pilrig Park on Sunday.
Officers are visiting businesses, community groups and churches in the hope of finding witnesses.
High-visibility patrols are continuing in the park area in a bid to reassure the public.
Inspector Kevin McLean said: “While a crime of this nature is rare, it has a significant impact upon the community and it is essential that we respond accordingly to address any concerns local residents may have.
“Our engagement with the community is also imperative for obtaining any relevant information for this inquiry.”